If an animal is bleeding, apply pressure with a ladies’ sanitary product on the wound to absorb the blood. After all, that is what they were created for. If, by chance, you have a clean baby diaper, that's even better.
If you do not have access to sanitary napkins or tampons and have a choice between toilet tissue, Kleenex and paper towels, go for the paper towels. Toilet tissue is made to disintegrate. Kleenex and related products are coated to make them gentle when you are blowing your nose 1,000 times a day. Paper towels boast being the "quicker picker upper" even if they are a different brand.
None of the above? Rip off the bottom of your t-shirt or even use a sock. Worry less about sterility than about stopping the bleeding. The vet will put your pet on serious antibiotics when things calm down anyway.